Generalized Boltzmann relations in semiconductors including band tails

Abstract

Boltzmann relations are widely used in semiconductor physics to express the charge-carrier densities as a function of the Fermi level and temperature. However, these simple exponential relations only apply to sharp band edges of the conduction and valence bands. In this article, we present a generalization of the Boltzmann relations accounting for exponential band tails. To this end, the required Fermi-Dirac integral is first recast as a Gauss hypergeometric function, followed by a suitable transformation of that special function, and a zeroth-order series expansion using the hypergeometric series. This results in simple relations for the electron and hole densities that each involve two exponentials. One exponential depends on the temperature and the other one on the band-tail parameter. The proposed relations tend to the Boltzmann relations if the band-tail parameters tend to zero. This work comes timely for the modeling of classical semiconductor devices at cryogenic temperatures for large-scale quantum computing.

References in corpus (1)

• Cryogenic Subthreshold Swing Saturation in FD-SOI MOSFETs described with Band Broadening

Cited by in corpus (3)

• Physics-Based and Closed-Form Model for Cryo-CMOS Subthreshold Swing
• Band tail formation in mono and multilayered transition metal dichalcogenides: A detailed assessment and a quick-reference guide
• $1/f$ noise in semiconductors arising from the heterogeneous detrapping process of individual charge carriers